Enterprisey is anything that is clearly part of the enterprise culture.
A culture where buzzy words are often used to talk about simple concepts but they do it that way so they can look smart inside that culture and impress outsiders.
The term enterprisey is used to be explicit on the criticism of such behavior.
PC guy: this is so cool, how did you improved this software?
mac guy: easy, I've added a delay of 3 seconds to every action and now users are feeling it's enterprisey
small business owner: I'm tired of presenting good projects and getting rejected, what's wrong with these people?
colleague: they only want their bloated, hyperexpensive projects approved because they're trapped in their enterpriseyness. The're surely saying one to each other: "hey, nobody got fired for hiring IBM"